Trigonometric Identities and Functions

This video tutorial covers the properties of trigonometric functions, focusing on reciprocal, quotient, and Pythagorean identities. It explains how to derive these identities and apply them to solve trigonometric problems. The video also discusses the significance of these identities in determining trigonometric function values and provides examples to illustrate their application.

Which of the following is a reciprocal identity for sine?

• sin(θ) = 1/sec(θ)

• sin(θ) = 1/cos(θ)

• sin(θ) = 1/cot(θ)

• sin(θ) = 1/tan(θ)

If cos(θ) = 2/3, what is sec(θ)?

• 3/2

• 2/3

• 1/5

• 5/2

What is the cotangent of θ if tan(θ) = 5?

• 1/5

• 5

• 1/2

• 2

Which identity represents tan(θ) in terms of sine and cosine?

• tan(θ) = cos(θ) / sin(θ)

• tan(θ) = sin(θ) / cos(θ)

• tan(θ) = 1 / sin(θ)

• tan(θ) = sin(θ) * cos(θ)

What is the Pythagorean identity involving sine and cosine?

• cos^2(θ) - sin^2(θ) = 1

• sin^2(θ) - cos^2(θ) = 1

• sin^2(θ) + cos^2(θ) = 1

• sin^2(θ) + tan^2(θ) = 1

If sin(θ) = 3/5 and θ is in the second quadrant, what is the sign of tan(θ)?

• Positive

• Negative

• Zero

• Undefined

Given tan(θ) = 5/12 in the third quadrant, what is the sign of sin(θ)?

• Positive

• Negative

• Zero

• Undefined

How do you find sin(θ) using the Pythagorean identity if cos(θ) = 3/5?

• sin(θ) = 1 + cos^2(θ)

• sin(θ) = cos^2(θ) - 1

• sin(θ) = 1 - cos^2(θ)

• sin(θ) = √(1 - cos^2(θ))

What is the value of r if x = -12 and y = -5 in the third quadrant?

• 12

• 17

• 5

• 13

If tan(θ) = 5/12, what is the value of sin(θ) in the third quadrant?

• -5/13

• 5/13

• -12/13

• 12/13